Question: Jessica is 2 times as old as Michael. Fourteen years ago, Jessica was 9 times as old as Michael. How old is Jessica now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Michael. Let Jessica's current age be $j$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $j = 2m$ Fourteen years ago, Jessica was $j - 14$ years old, and Michael was $m - 14$ years old. The information in the second sentence can be expressed in the following equation: $j - 14 = 9(m - 14)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $m$ and substitute it into our second equation. Solving our first equation for $m$ , we get: $m = j / 2$ . Substituting this into our second equation, we get: $j - 14 = 9($ $(j / 2)$ $- 14)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 14 = \dfrac{9}{2} j - 126$ Solving for $j$ , we get: $\dfrac{7}{2} j = 112$ $j = \dfrac{2}{7} \cdot 112 = 32$.